I came across this question while applying to a teacher training program called EnCorps. I liked it so much I think I'll share it with you.
As a successful professional, how have you used math or science in your daily work? What would you say to a student who questioned whether math or science would be useful in their future? How will you communicate that with students in a classroom?
As the owner of a private math tutoring business, I use math in my work everyday - and not just in the ways you would expect. I use skills from Pre-Algebra to help my students calculate their grade percentages,, to determine how much a $60 lesson would be at 25% off, and to do my taxes. Algebra helps me show students how to calculate the scores they need on their upcoming tests to get the grade they want. The concepts of logic introduced in Geometry help me to reason my way through difficult problems both in mathematics and in my everyday life. Algebra 2 skills help me schedule my students efficiently,...
As you may know, I am a big fan of the well-known author and brain specialist, Dr. Daniel Amen. He mentions in several of his books that Physical Exercise is good for the brain. I have read of research studies that showed a clear correlation between IMPROVEMENT in students' test scores in math and science, and their level of physical activity (for example, when math class followed PE class, the students had significantly higher scores). Maybe we should schedule PE before all math classes in our schools. What do you think about that idea?
This morning I read an online article on the myhealthnewsdaily site, entitled "6 Foods That Are Good for Your Brain," and another article about how Physical Exercise helps maintain healthy brain in older adults too. The second article, "For a Healthy Brain, Physical Exercise Trumps Mental Workout" was found under Yahoo News.
The remainder of this note is quoted from that article:
Regular physical exercise appears to...
I've managed to tutor a number of students this year and it has all been very rewarding and enjoyable. Every now and then, I have seen the proverbial light bulb go off in a student's mind when they start to grasp the subject. It's moments like this that I feel very lucky to have such an opportunity to work with students. It's a really enjoyable experience for me as a tutor and it's a bit reason why I decided to be a tutor. Whether it is assisting with homework or discussing mathematical ideas and concepts, I'm very interested in helping your son or daughter improve their skills and abilities in math.
Visualize, verbalize, mathematize!
I've been asking students the following question for years: "Why do you show so little work, and where are you completing the problem?" Most students I have worked with write less down than I do, and I have quite a bit of math under my belt. I still have not found the answer to this question. Some students say it’s because they don’t see the point, but they have been cheated if teachers have given them credit for answers without work. As math gets complicated there is more and more work that needs to be done, and if a student has bad habits of doing mental math, then this will be a hindrance to success.
These are things that all students of higher mathematics should do:
1. Write the original problem down. When solving problems you want to make sure that you are staring at the actual problem. You don't want to look at your paper and then back to the book or sheet of paper that the problem is on.
2. Show your work just like your teacher does when they are introducing...
I used to be a great math student. It would come naturally me, I never really had to "study" for the tests to get my A's. This all took a turn when I took PreCalculus in Highschool. I remember getting my first test back and seeing a 67/100. I was horrified! I was in shock! When my mother found out, she repeated her famous line "Practice makes Perfect!" She made me sit down with my textbook. She made me start from page 1 of the textbook. She told me to read every single word on the page including the captions under the pictures. She also made sure I did every single example problem and all the practice problems, yes all 97 of them (that was just for one section of the chapter). After doing this for 2 days. I took my next math test.
When my teacher was handing back the test I prayed I at least would get a B! But I was in for a surprise...I received 93/100. My teacher was so happy with my improvement she had put smiley faces all over the page! I couldn't believe...
Occasionally, parents demand “worksheets”. I have a tepid reaction to that request. First, I personally believe that a tutor is not meant to be a “worksheet provider”. Sometimes parents want their child to be “drilled” into learning. Those parents may feel that the only way to acquire skills and/or knowledge is to force it into their child’s psyche by repetitious action – worksheets. Most parents do recognize that a tutor has excelled in a particular area of study, but some still trust education to the worksheet. A thesaurus lists as synonyms for “tutor” the words: coach, educator, guide, mentor, and instructor. (Nothing about “worksheet provider”!) Nevertheless, parents still get “hung-up” on worksheets, and demand “lots of them”. From a purely educational stance, worksheets can be used only one way. Worksheets are generally considered to be convergent materials by professional educators.Worksheets lead students to believe that there is only a single correct way to use them, and worksheets...
If you get stuck doing homework problems often, have a hard time doing your classwork, or sometimes you just can't follow your lecture notes try going to Wolfram Alpha. Wolfram Alpha is a computational knowledge engine that is designed to handle mathematical problems and computation, and scientific problems. It has its limitations but it is a really awesome tool that gives a lot of detail when you need it. Try it out for yourself.
My wife is worried about me because I was tutoring in my dreams last night.
This has been a great summer!
I recently found out that one of the great kids I tutored in Geometry last school year got a 96 on his final exam! I could not be more proud!
For the second summer in a row now, I have tutored math to prepare my students for the upcoming school year. I have come to realize that the best way to help get the material across to my students is through games. Both summers I have managed to come up with many different games that tie right in with the material which we are covering and they all make a huge difference in how well the student understands the concepts.
Not only do my students have fun while learning, but I have to admit that I have just as much fun making up the games and playing them with the students!
I am all geared up for this coming school year and can’t wait to get my students started off on the right foot!
Over the past couple of years, I have found myself more and more often recommending graphing calculators for Algebra 1 students. This wizard instrument, capable of far more than I myself know how to tap into, works well with my tutoring style. However, I have seen firsthand what the consequences can be when students learn to use them without guidance. So many times, I have worked with high school upperclassmen and college students who cannot perform basic operations with fractions, graph by hand, evaluate an expression by hand, or perform addition and subtract with positive and negative integers because they became reliant on their calculators before ever properly learning the skills. These students usually lack the time or motivation to go back and learn how to do the skills by hand. Their courses move along rapidly and they need to spend their tutoring time keeping pace with the more advanced ideas. This is particularly unfortunate because these are the same skills they are most...
Playing a math game. Following a recipe. Building a science project, robot, or electronic kit... These are some ways to use hands-on learning activities to make science and math more interesting. This summer, for example, I have been using some new modules that include electronics/science of electricity, automotive engine technology, solar energy labs, etc. for "gifted", "average", and "special needs" students. And everybody loved the new study lessons. Even the ADD/ADHD students (myself included) stayed interested during entire lessons.
I think we need more of this sort of thing in the schools. What do you think? If hands-on learning can keep the attention of ADD/ADHD students, it can work for other students too! I enjoy watching students learn through interactive games that utilize technology. For example, we like to race the clock and fill in math and science puzzles. There are many active ways to make learning more interesting, and before you know...
Keeping students motivated during the summer months starts in the proceeding school year. As students are exposed to a broadening of subjects, each student will naturally like one or two. The motivation comes when a teacher or parent recognizes the interest and then turns the student toward further investigation / discovery. The student will experience the joy of learning, which once experienced will motivate the student to learn more. Facilitating that desire will keep the student on track year round.
The best way to learn and study for tests is to use technology. Websites like StudyIsland give you a chance to run through subject matter sample questions, at 10 or 15 or 20 at a time. Studies show that repeated scores averaging say 80%, result in a most probable 70% on the actual quiz, test, exam taken. The good news is you can practice online until you have command of the topic. As your average goes up so does your probable quiz, test, exam score go up. The bad news is that it costs to use Websites like StudyIsland. As a tutor I have my own access which I will let you use while I am tutoring you.
I'm a new tutor to this site. Within the past few days, I've been working on getting certified in as many subjects as possible. These are all of the subjects I'm certified to tutor in on the website. Most of the subjects are in math or science. Some are in English topics as well like in reading and writing, etc. I also am certified to tutor to prepare for a lot of standardized tests and a few common computer software programs people use. Please read my profile if you need a new tutor in the Hillsboro or Portland area!
A few things that I did as a child and which I have found help the students with whom I work prepare for the new school year are: reading many genres daily, doing crossword and other pencil-and-paper puzzles daily, reviewing the notes from the past year, and keeping a journal of all activities and daily occurrences. Subscribing to new journals and magazines in July also is great because by the time September rolls around, the student is anticipating an arrival and is anxious to share the contents of the publication/publications with peers.
Summertime ... swimming, reading, barbeques, hanging with friends. Summer jobs and going out after work. Yet for some, schoolwork and studying are a big part of our summer agenda.
No matter what time of year you are studying, it is crucial to know when to stop and take a break. Forcing your attention past your limit will not be productive. If you can't summarize what you just read, you have read too long. If you are making more mistakes on your math homework, it's time to do something else.
What's your ideal study session? It might be an hour or two, or it might be only 20 minutes. Stick to the length of time that works best for you. When you come back refreshed, you will learn more easily.
Get into the slower summertime pace. When the fall comes, remember to stop studying and do something else, even if only for a few minutes. Your brain will thank you.
Flash cards -- highlighting -- writing down definitions. Do you do all that and still have low test scores? Often, straight memorization is not enough to really learn the subject well.
For example, in biology you may learn that proteins are formed from peptide chains. You may also learn that a polymer is a chemical compound that has repeated units. But if an exam question refers to a "polypeptide," you might not realize that it was talking about a protein.
The key here is to make associations. What are polymers? What type of biological compounds can be classed as polymers? "Poly" means "many." So, a polypeptide would be "many peptides." What compound is composed of many peptides? A protein, of course.
This type of reasoning is not developed by straight memorization. You need to reach for the meaning. Make lists, tables, or diagrams; look up words; make links and associations. Write definitions in your own words only. Don't guess....
I'll start off with something simple here. A tool that I have found incredibly useful when trying to check my work is WolframAlpha (http://www.wolframalpha.com/). I can't tell you how many students I've had tell me that it's been a life-changer. Just type in an equation, and it will give you graphs, solutions, alternate forms, and much more. This is especially useful for higher level math and graphical analysis.
Here's an interesting math fact: the sum of any sequence of odd numbers from 1 to n is always a perfect square.
1 = 1
1+3 = 4
1+3+5 = 9
1+3+5+7 = 16
1+3+5+7+9 = 25
1+3+5+7+9+11 = 36
The sum is actually the square of (n+1)/2.
What this also means is that every odd number can be expressed as a difference of consecutive squares:
1-0 = 1
4-1 = 3
9-4 = 5
16-9 = 7
25-16 = 9
36-25 = 11
In this case, each odd number n can be expressed as the square of (n+1)/2 minus the square of (n-1)/2.
You can now use this knowledge to derive an infinite number of Pythagorean triples. For each odd number n greater than 1, these three values comprise a Pythagorean triple: n, (n^2-1)/2, (n^2+1)/2
3, 4, 5
5, 12, 13
7, 24, 25
9, 40, 41
11, 60, 61
13, 84, 85
Because of the relationship of the numbers,...